Why is my oil signal keeps buzzing on my speedometer?

It isn't too hard a job it's just a messy one. The oil filter type might depend on the version of the engine yours is fitted with. This method is for the basic 'screw on' type.
I have attached a series of videos that will be a rough guide to doing this job.
Raise the front of the vehicle and support it on axle stands. The drain plug will be a larger size bolt on the lowest part of the sump, (oil pan), on the engine.
I usually use a large sheet of cardboard on the floor with an oil catch pan on top of it.
Carefully loosen the drain plug one turn. It should start to leak oil. Gently remove the plug 'by hand' so you don't drop it in the oil pan with the used oil. Let it drain until it's a steady Slow drip. Clean the drain plug and the hole it came out of then refit the plug.
**NOTE** fit the plug by hand until it stops THEN just turn it a small amount tighter with a spanner or socket. It does NOT need to be in super tight, about 20 to 25Nm as a torque setting.
Dispose of the old oil safely. Some mechanic shops will accept it for safe disposal.
Facing the rear of the vehicle and looking down on the engine, the filter should be on the left side about half way down. Remove it from underneath as access will be better. It should only be in 'Hand Tight' but you might need a 'strap' or 'filter' tool to loosen it at first.
** The filter will have oil in it and oil will leak out of the filter mount hole so use your drip pan to catch the spillages**.
Make sure you have the old filter oil seal ring as they sometimes stay stuck to the engine block.
Clean all the exposed faces as best you can. Pour a small amount of oil into the filter and rub a small amount of oil over the new oil seal ring to stop it wrinkling up when you re-fit it. Re-fit the new filter by hand until it is nice and tight.
**NOTE** This is tight enough. You don't need a tool to tighten it!
Check the sump plug is refitted and the oil filter is in place. Wipe clean any spills made during refitting.
Check your owner's manual for the type and amount of oil needed and refill the engine. Once filled walk away for about ten minutes before you check your oil levels. When it is correct start the engine, let it settle into a smooth idle then check under the vehicle for leaks from the sump plug and the filter housing. No leaks means a good job done. Lower the vehicle back onto the ground.
Give it two or three days of use and re-check for leaks and your oil level. No leaks and a steady oil level is a job well done. https://www.carcarekiosk.com/video/2002_Kia_Sportage_2.0L_4_Cyl._Sport_Utility_(4_Door)/oil/change_oil_and_oil_filter

Run the engine for 10 minutes to warm the oil, remove the sump bung from underneath the car, located on the sump. Try searching youtube for a helpful video before you try attempting this yourself

Engine oil: Drain or extract and replenish; renew oil filter Engine oil: Drain or extract engine oil ? Chapter. Renewing oil filter ? Chapter. Replenishing engine oil ? Chapter. Draining or extracting engine oil Special tools and workshop equipment required t Used oil collection and extraction unit -V.A.G 1782- t Oil spill cloth -VAS 6204/1- Draining or extracting engine oil Carry out the following procedure: > Note
t For engines with standing oil filter the oil filter must be renewed before changing the engine oil. When removing the filter element a valve is opened, the oil in the filter housing automatically flows into crankcase. t If the engine oil is drained and not extracted with an oil extractor, replace drain plug. This prevents leaks. t Observe disposal regulations! - Extract engine oil using used oil collection and extraction unit -V.A.G 1782-. or - Remove oil drain plug. - Let engine oil drain. > Note
t The oil drain plug is fitted with a secure seal, therefore the oil drain plug must always be renewed. t Observe disposal regulations! - Screw in new oil drain plug with seal hand-tight. - Replenish engine oil, specification ? Chapter. Engine oil capacity: "Power unit" ? Power unit; Rep. Gr.17"Lubrication; oil capacities" or ? Maintenance table. Specified torques for oil drain plug: t Petrol and diesel engines 30 Nm > WARNING
t Torque specifications must not be exceeded. t Excess torque can cause leaks in the area of the oil drain plug or even damage. Renewing oil filter Renewing oil filter, 1.4 l and 1.6 l injection engines > Note
t Prevent engine oil from dripping onto components in engine compartment. t Oil new O-rings before installing. t Observe disposal regulations! Renewing oil filter, 1.4 land 1.6 l engine Carry out the following procedure: alt="W00-10211"> - Unscrew cover cap -1- with socket insert 36 mm AF and remove cover with oil filter insert -4- and valve -5-. - Renew O-ring -2- of cover cap and O-ring -3- of valve. - Renew used oil filter element with new filter element. > Note
Observe disposal regulations! - Tighten cover cap -1-. Cover cap torque setting: 25 Nm. Replenishing engine oil Oil specifications ? Chapter Engine oil capacities: "Power unit" ? Power unit; Rep. Gr.17"Lubrication; oil capacities" or ? Maintenance table. General notes > Note
Observe disposal regulations! - After replenishing with oil, wait at least 3 minutes and then check oil level. - Pull out dipstick, wipe with a clean cloth and push dipstick in again to limit stop. - Pull dipstick out again and read oil level. alt="N01-10183"> For dipstick as illustrated: A - Oil must not be replenished. B - Oil may be replenished. It may happen that the oil level afterwards is in the -A- region. C - Oil must be replenished. It is sufficient if the oil level is in the -B- region (hatched area) afterwards. There is a danger of damaging the catalytic converter if the oil level is above the -A- marking. - If oil level is below -C- marking, top-up oil to -A- marking. alt="N01-10255">

If its still leaking from the pan gasket then replace the pan and also check if the PCV positive crank case valve is NOT blocked as there could be lot of pressure building up in the engine.

The oil turning black and dirty means that besides doing its primary job (engine lubrication), your oil is doing very well at its second job, which is removing contaminants, exhaust by-products, and even microscopic pieces of metal (caused through normal engine wear and tear) from your engine, and bringing them around to be deposited in your oil filter and oil pan. In short- it is cleaning your engine.
It is possible that the previous owner of your Pajero did not change their oil often enough, and your fresh oil change removed allot of build-up.
Remember- this is all stuff that was in your engine, and is not anymore! Keep changing your oil and filter every 3,000 miles (4500 km) or so,, and over time you will see the used oil getting cleaner as it does the same for your engine!

The warning light is for oil pressure.

First check the dipstick, make sure there's enough oil in the engine.
If so, then there may be a problem with the oil filter, when was it last changed.
It could be the sender, is the connection good and clean.
Finally the oil pump filter may be blocked, or possibly the oil pump has failed.

The following procedure explains how to change the oil, and filter.

1. Before changing the oil, see that the vehicle is situated on a flat surface with the engine warmed; warm oil will flow more freely from the oil pan.
2. Turn the engine OFF, open the hood and remove the oil filler cap from the top of the engine valve cover. CAUTION
   Hot oil can burn you. Keep an inward pressure on the plug until the last thread is cleared, then, quickly remove it.
   
3. Place a container under the oil pan large enough to catch the oil. A large, flat drain pan is the most desirable.
4. Remove the oil drain plug. Allow the oil to drain completely.
5. When the oil has finished draining, install the drain plug, then tighten until just snug. Use a new washer (if applicable) on the plug.
6. Move the oil drain pan or use a second pan under the oil filter; the filter retains some oil which may drain when it is removed.
7. Using an oil filter wrench, loosen the filter by turning it counterclockwise, then unscrew it by hand.
8. Using a clean cloth, wipe the filter mounting surface of the cylinder block. Apply a thin coat of clean oil to the new filter gasket and install the filter by hand carefully threading it on turning clockwise. Tighten it as much as you can by hand, then use the wrench to turn it an additional 1/2 to 3/4 turn.
   
9. Remove the drain pan from under the engine. NOTE: Used engine oil is an extreme environmental hazard. Proper disposal of used engine oil is very important. Rather than dumping the oil in storm drains or throwing it in the trash, you should take it to an approved recycling center. Many shops will accept used engine oil. If you are uncertain where to take the oil, many local municipalities can direct you.
   
10. Add the correct amount of recommended oil into the filler hole on top of the valve cover. Be sure that the oil level registers near the full line on the oil dipstick.
11. Install the filler cap. Start the engine without touching the accelerator pedal and allow it to idle. The oil pressure light on the instrument panel should go out after a few seconds.
12. Run the engine for 1-2 minutes and check for leaks. Turn the engine OFF, then, after a few minutes, recheck the oil level; add oil. Be sure to check for oil leaks. If you find any, correct them immediately.
13. Recheck and/or refill the engine with oil. NOTE: If the filter leaks, make sure the old filter gasket is not on the mounting flange. If the old gasket is not on the flange, tighten the filter a little more. If it still leaks, try another filter.
    

CHECK ENGINE OIL LEVEL ON OIL DIP STICK.OIL LEVEL SHOULD BE ON FULL MARK IF NOT ADD OIL UNTIL YOU GET TO FULL MARK.IF OIL LEVEL OKAY.YOUR LOW OIL PROBLEM CAUSED BY WORN DAMAGED OIL PUMP OR WORN ENGINE CRANKSHAFT BEARINGS.IF OIL HAS NOT BEEN CHANGED A LONG TIME CHANGE OIL AND OIL FILTER NOT GUARANTEE TO FIX PROBLEM.BUT COULD BE MINOR THING.OIL FILTER COULD BE STOPPED UP.WEAKEN OIL FLOW BUT LIKE I SAID PROBLEM COULD BE OIL PUMP OR ENGINE BEARINGS.REMOVE OIL SENDING UNIT SCREW IN A OIL PRESSURE GAUGE.TURN ENGINE OVER SEVERAL REVOLUTIONS TO SEE IF OIL PRESSURE BUILD UP TO 40 LBS. SEE 40 - 60 PSI. 2000 RPM.IF NO OIL PUMP TO WEAK .IF OIL PRESSURE RISES WHEN TURN ENGINE OVER.I HAVE SEEN FAULTY OIL PRESSURE SENDING KEEP ENGINE FROM RUNNING BECAUSE OIL PRESSURE SENDING UNIT WILL DISABLE FUEL PUMP RELAY TO KEEP FROM DAMAGING THE ENGINE.

I would think you need to connect that cable up, it will go from the back of the speedometer head, thru the firewall and down under the van to the driver side rear of the transmission, if it doesn't have cruise control, if it does, there will be a cable from the speedometer head to a box, usually in the engine compartment, where another cable will run from that box to the driver side rear of the transmission. The oil filter should be at the back of the driver side of the motor, underneath. The air filter should be on top of the throttle body, there should be enough room to get to it by removing the "doghouse" cover inside the van. I would consider replacing the fuel filter, tranmission fluid and filter. A set of spark plugs wouldn't hurt too.Take a look at the anti-freeze color. Also, check for any leaks once you get it going.

Drain the crankcase oil into a clean container in which you are able to measure the amount. Replenish this amount up to the quantity stated in your hand book. Remove dipstick and fill the crancase with just this oil. Dip the oil level and using a scriber or a file, mark the dipstick at the level of the oil.
Notes:
1. The quanity of oil is the engine capaity less the oil filter.
2. You may wish to use clean new oil and fit a new filter. If so, use the fill capacity including the oil filter, or add about another pint.